The generator matrix

 1  0  0  0  0  1  1  1  1  X  1  1  1  1  1  1
 0  1  0  0  0 2X  1 2X+1  2  1  2 2X+2 X+2  X 2X 2X
 0  0  1  0  0 2X+1  2 X+1  X X+2  2 X+2 2X  0 X+2  1
 0  0  0  1  0 2X+2  2  1 X+1  1  X  2 2X 2X+2  X  1
 0  0  0  0  1 2X+2  1  X 2X+1 2X+2 2X+2 2X X+1 X+2  1 X+2

generates a code of length 16 over Z3[X]/(X^2) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+126x^22+324x^23+692x^24+936x^25+1416x^26+2214x^27+2322x^28+4578x^29+5266x^30+6138x^31+8388x^32+6996x^33+5814x^34+5946x^35+3824x^36+1890x^37+1218x^38+674x^39+270x^40+16x^42

The gray image is a linear code over GF(3) with n=48, k=10 and d=22.
This code was found by Heurico 1.16 in 8.02 seconds.